But that would be a tough sell for many conservatives in Congress, where some lawmakers until recently were trying to take away TSA agents’ badges.

The fatal shooting of Gerardo Hernandez and the ensuing gunfight at LAX called attention to a long-running debate over the powers of TSA, whose screeners aren’t considered law enforcement officers even though many of them wear badges. The 39-year-old Hernandez was the first TSA officer killed in the line of duty in the agency’s history.

Both lawmakers and the Obama administration have called for reviewing airport security procedures after the shooting spree. But union officials are already offering a concrete proposal: create a new category of TSA agent in addition to the 45,000 existing screeners. People in the new positions would be law enforcement officers, who could carry handcuffs and firearms as well as make arrests.